In mass spectrometry, we ionize an analyzed sample by a suitable method, separate generated ions based on the difference in the mass-to-charge ratio, and detect them qualitatively or quantitatively by their respective mass-to-charge ratios. By this method we can get information about the composition and the structure of the analyte. Here, we define the term, mass-to-charge ratio of a given ion, as follows, and use it throughout the present Description. Its mass m is divided by the atomic mass constant ( 1/12 of the mass of one atom of 12C) to yield its exact relative mass, which is further divided by its charge number zi. The resultant dimensionless number is its mass-to-charge ratio.
A mass spectrometer consists of an ion source, an ion introduction unit, a mass analyzer, an ion detection unit, etc., and a passage of ions is in high vacuum at least in the mass analyzer and around it. The mass analyzer separates ionic species having different mass-to-charge ratios with each other by the difference in their motion in the vacuum. Most of spectrometers of general use which are now on the marcket have one of three types of mass analyzers described below (see Non patent Literature 1-4). Hereafter, we use the term, crude ions, to refer to a crowd of ions which is dealt with as a group at various locations in a mass spectrometer, in order to distinguish from one ion or merely plural ions. We also use the term, initial state, to refer to a kinetic state of an ion in the ion source before extraction by an acceleration voltage. Furthermore, we use symbol e which represents the elementary charge, and use the International System of Units (SI) as units for physical quantities unless we explicitly state otherwise.
<Time-of-Flight (TOF) Mass Analyzer>
In a TOF mass analyzer, pulsed crude ions are extracted from an ion source by a predetermined acceleration voltage U, and are introduced into a field-free drift path of known length LF. From the velocity of each ion v, the time TF needed for the ion to travel through this path is given by the next formulaTF=LF/v. Hence the TOF analyzer functions as a velocity analyzer.
<Magnetic Sector Mass Analyzer>
In a magnetic sector mass analyzer, crude ions are extracted from an ion source by a predetermined acceleration voltage U. Then these ions are introduced into a magnetic sector analyzer, perpendicular to a homogeneous magnetic field of the magnetic flux density B. In the magnetic field the flight direction of each ion is continuously altered by the Lorentz force. Consequently, the ion travels on a circular path of a radius R. This radius is given by the next formulaR=mv/zieB. 
Hence the magnetic sector analyzer functions as a momentum analyzer.
<Quadrupole Mass Analyzer>
A quadrupole mass analyzer consists of four samely shaped rod electrodes. The quadrupole electric field is produced in the long and slender space surrounded by these electrodes, and this space is used as a passage of ions. Crude Ions are introduced into the passage from one end in the longitudinal direction along with the symmetry axis. Then each ion travels toward the other end by inertia, and besides oscillates by the force received from the electric field. In this time, only an ionic species of a particular mass-to-charge ratio is fit for the electric field, and may travel the passage to the exit end with stable oscillation of limited amplitudes. The other ionic species oscillate with too large amplitudes, and are removed either with hitting the rod electrodes or with flying out between the rod electrodes.
In addition to the above, there are on the market mass spectrometers which have a linear quadrupole ion trap mass analyzer, a three-dimensional quadrupole ion trap mass analyzer, or a Fourier transform ion cyclotron resonance mass analyzer. These ion trapping type devices, however, require somewhat complicated operation for one analysis. This operation consists of introduction, tpapping and ejection of ions. Moreover, since the analysis becomes intermittent, it is not suitable at least for fast real time measurement. Consequently, these mass spectrometers are used mainly for a use in which their ion trapping function is effective.